/*
 * @lc app=leetcode.cn id=37 lang=cpp
 *
 * [37] 解数独
 *
 * https://leetcode.cn/problems/sudoku-solver/description/
 *
 * algorithms
 * Hard (67.56%)
 * Likes:    1384
 * Dislikes: 0
 * Total Accepted:    168.3K
 * Total Submissions: 248.8K
 * Testcase Example:  '[["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]'
 *
 * 编写一个程序，通过填充空格来解决数独问题。
 * 
 * 数独的解法需 遵循如下规则：
 * 
 * 
 * 数字 1-9 在每一行只能出现一次。
 * 数字 1-9 在每一列只能出现一次。
 * 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）
 * 
 * 
 * 数独部分空格内已填入了数字，空白格用 '.' 表示。
 * 
 * 
 * 
 * 
 * 
 * 
 * 示例 1：
 * 
 * 
 * 输入：board =
 * [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]
 * 
 * 输出：[["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
 * 解释：输入的数独如上图所示，唯一有效的解决方案如下所示：
 * 
 * 
 * 
 * 
 * 
 * 
 * 提示：
 * 
 * 
 * board.length == 9
 * board[i].length == 9
 * board[i][j] 是一位数字或者 '.'
 * 题目数据 保证 输入数独仅有一个解
 * 
 * 
 * 
 * 
 * 
 */

// @lc code=start
class Solution {
public:
    void solveSudoku(vector<vector<char>>& board) {
        for (int i = 0; i < 9; ++i) {
            for (int j = 0; j < 9; ++j) {
                if (board[i][j] != '.') {
                    visited[i / 3][j / 3][board[i][j] - '0'] = true;
                    visitedLeft[j][board[i][j] - '0'] = true;
                    visitedRight[i][board[i][j] - '0'] = true;
                }
            } 
        }

        dfs(board, 0, 0);
        board = res_;
    }
private:
    vector<vector<char>> res_;
    bool visitedLeft[9][10] = { false };
    bool visitedRight[9][10] = { false };
    bool visited[3][3][10] = { false };

    void dfs(vector<vector<char>>& board, int x, int y)
    {
        if (x == 9) {
            res_ = board;
            return ;
        }

        char ch = board[x][y];
        if (res_.size() != 0) {
            return ;
        }
        if (ch != '.') {
            dfs(board, x + (y + 1) / 9, (y + 1) % 9);
        } else {
            for (int i = 1; i <= 9; ++i) {
                if (!visitedRight[x][i] && !visitedLeft[y][i] && !visited[x / 3][y / 3][i]) {
                    visited[x / 3][y / 3][i] = true;
                    visitedLeft[y][i] = true;
                    visitedRight[x][i] = true;
                    board[x][y] = '0' + i;
                    dfs(board, x + (y + 1) / 9, (y + 1) % 9);
                    board[x][y] = '.';
                    visited[x / 3][y / 3][i] = false;
                    visitedLeft[y][i] = false;
                    visitedRight[x][i] = false;

                }
            }
        }
    }
};
// @lc code=end

